Mathematical Sciences: Problems in Crystal Growth and Equilibrium Shapes

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Crystal equilibrium and growth problems involving anisotropic surface energy and/or mobility will be investigated, with and without diffusion. New theoretical frameworks for considering such problems will be developed, as will new algorithms and computer programs for computing their solutions. In particular, the crystalline approach will be further developed and applied to new problems. In this context, variational problems often become finite dimensional, and parabolic partial differential equations for surface motion become systems of ordinary differential equations. The general context for this work is geometric measure theory.